Combining Imprecise or Conflicting Probability Judgments: A Choice-Based Study

Abstract

This article develops a new approach to study the impact on beliefs and decisions of uncertain probability forecasts by advisors. The core concept of that approach, which builds on the revealed-preference approach favored by economists, is the one of revealed beliefs - the precise probability leading to the same choice as an uncertain probability forecast. The paper defines two properties of revealed beliefs - pessimism and likelihood sensibility - and allows them to vary as a function of the source of uncertainty. It then focuses on the impacts on revealed beliefs of two uncertain contexts of intense practical importance, namely consensual but imprecise uncertainty (Si) and conflicting uncertainty (Sc). In the first case, the advisors agree on the same imprecise probability forecast whereas in the latter case the advisors disagree on the probability of the same risk and the decision-makers receives two precise but different probability forecasts. Two experiments test a series of predictions concerning the impacts on revealed beliefs of each uncertain context. The results of both studies show that revealed beliefs vary as a function of the source of uncertainty, in particular for low and high probability events. The second study tests a series of predictions on the differences between revealed beliefs and the beliefs that decision-makers report as their best estimate of the probability of the risk (called judged beliefs).

Keywords: sources of uncertainty, beliefs, experts, aggregation, cumulative prospect theory